Median Trajectories

  • Kevin Buchin
  • Maike Buchin
  • Marc van Kreveld
  • Maarten Löffler
  • Rodrigo I. Silveira
  • Carola Wenk
  • Lionov Wiratma
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6346)


We investigate the concept of a median among a set of trajectories. We establish criteria that a “median trajectory” should meet, and present two different methods to construct a median for a set of input trajectories. The first method is very simple, while the second method is more complicated and uses homotopy with respect to sufficiently large faces in the arrangement formed by the trajectories. We give algorithms for both methods, analyze the worst-case running time, and show that under certain assumptions both methods can be implemented efficiently. We empirically compare the output of both methods on randomly generated trajectories, and analyze whether the two methods yield medians that are according to our intuition. Our results suggest that the second method, using homotopy, performs considerably better.


Span Tree Time Stamp Dynamic Time Warping Medial Axis Homotopy Type 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Kevin Buchin
    • 1
  • Maike Buchin
    • 2
  • Marc van Kreveld
    • 2
  • Maarten Löffler
    • 3
  • Rodrigo I. Silveira
    • 4
  • Carola Wenk
    • 5
  • Lionov Wiratma
    • 2
  1. 1.Dept. of Mathematics and Computer ScienceTU Eindhoven 
  2. 2.Dept. of Information and Computing SciencesUtrecht University 
  3. 3.Dept. of Computer ScienceUniversity of CaliforniaIrvine
  4. 4.Dept. de Matemàtica Aplicada IIUniversitat Politècnica de Catalunya 
  5. 5.Dept. of Computer ScienceUniversity of Texas at San Antonio 

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